# Sample size for Attribute data – Rule of Thumb

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• #38536

Parth
Participant

Can anyone explain the following rule of thumb for estimating a minimum sample size for attribute data as taught to us by a Master Black Belt?:
np > 5
n = sample size
p = proportion defective
So if you wanted to estimate a sample size and you knew that you had a 1% defect rate (p = 0.01), you’d need to take a minimum of sample size of 500.  I can’t work out where this rule of thumb comes from, what the assumed confidence level is, etc.

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#115300

Tim F
Member

I’m not sure why *your* MBB likes this rule of thumb ;-) but I can come to a couple of conclusions why this would be a good number. When np > 5, then the normal approximation is pretty good, which is a useful thing for all sorts of calculations. 5, then the normal approximation is pretty good, which is a useful thing for all sorts of calculations. 5, then the normal approximation is pretty good, which is a useful thing for all sorts of calculations.Another feature is of this rule of thumb is related to the standard deviation and confidence intervals. Whether you officially have a Poisson distribution or a binomial distribution, the standard deviation will be pretty close to np^0.5 = 5^0.5 = 2.2. The 95% confindence interval would run from roughly 5 +/- 4.4, which does not include 0. So if you get 0 defect, you can be pretty sure it is better than 1%.
On the other hand, getting double the expected defect rate is evidence of slipping performance.On the other hand, if np = 4, the 95% confidence interval runs basically from 0 to 8, so even getting zero defects is not strong evidence of improvement.
And getting double the defects is still not a strong sign of bad performance.
Tim F

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#115302

Mikel
Member

Go pick up a copy of Juran’s QC Handbook and fire your MBB.

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#115307

Parth
Participant

Hmmm… I’ve got lots of  “QC Handbook” type guides and textbooks.  Couldn’t find any explanations in any of these.  Looked up the web using Google, couldn’t find any explanation, searched isixsigma – couldn’t find any explanation.  Must be some somewhere though…
:-)

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#115310

Mikel
Member

Go find the chapter on statistical methods in Juran’s handbook and find the info on when it is appropriate to approximate one distribution with another.

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#115318

Jürgen De Cock
Participant

The following book explains (next to a lo of other stuff) how to calculate sample sizes.
Implementing Six Sigma by Forrest W. BreyfogleIII.ISBN 0-471-29659-7 (second edition) I know know there is a third edition.
page 310 – 320 handels about it.
generally spoken a verry good book.

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